Mathematics

When you insert geometric means between two numbers, you're building a geometric sequence where each term is a constant multiple of the previous one. Here, you need to find the common ratio $r$ that makes the sequence $3, a, b, 24$ work—then identify $b$. The key is using the fact that in a geometric sequence, the ratio between consecutive terms is always the same, so you can set up an equation relating the first and last terms through the number of steps.

When you insert geometric means between two numbers, you're building a geometric sequence where each term is a constant multiple of the previous one. Here, you need to find the common ratio $r$ that makes the sequence $3, a, b, 24$ work—then identify $b$. The key is using the fact that in a geometric sequence, the ratio between consecutive terms is always the same, so you can set up an equation relating the first and last terms through the number of steps.